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Extend KEH framework to differential rotation

Develop a fully general relativistic computational framework within the Komatsu–Eriguchi–Hachisu (KEH) method to model axisymmetric neutron stars with differential rotation by solving the angular momentum relation j(Ω) = A^2(Ω_c − Ω) (Eq. 39) self-consistently, rather than imposing the rigid-rotation limit Ω = Ω_c, to obtain equilibrium configurations for finite A.

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Background

The paper models rapidly rotating neutron stars using the KEH method but restricts to rigid-body rotation (large A, Ω = Ω_c). The authors note that correctly describing differential rotation requires a self-consistent iterative solution of the j(Ω) law, which they do not implement here.

They emphasize that extending their fully relativistic calculations to differential rotation is important for exploring more realistic rotation profiles and potentially different maximum masses and stability properties, but they defer this extension.

References

To correctly describe differential rotation in a fully general relativistic framework, Eq.~39 should be solved through a self-consistent iterative procedure. In the present study, however, we restrict ourselves to the limiting case of large $A$, which corresponds to rigid-body rotation, i.e., $\Omega = \Omega_c$. We will focus on exploring the relationship between rotational effects and properties of the nuclear equation of state, leaving the extension to differential rotation for future work.

— Fully general relativistic description of rapidly-rotating axially-symmetric neutron stars for constraining nuclear matter equations of state (2505.20990 - Kwon et al., 27 May 2025) in Section FORMULATION, Modeling of neutron star structure — Rotating case